What makes you think that the MTBF of the arduino board has been characterized? MTBF is typically characterized (at considerable testing expense) for industrial products, but the arduino is a development and prototyping platform targeted at hobbyists and educational market.
The MTBF of the arduino board itself is also not very useful, since the MTBF will be impacted by what it's connected to - and maybe even what code it's running. An arduino micro board just sitting not connected to anything should have an essentially indefinite lifespan (the full sized boards use electrolytic caps, which do have a limited lifetime, but the micro doesnt), barring abuse; it's not like a mechanical device that experiences wear and tear and is expected to fail after some length of time.